The increasing uncertainty due to advances in modern systems has negatively impacted system health and safety. System health and safety problems associated with uncertainty can be attributed to (1) inadequate system design, (2) ill-suited controller and operating envelope, and (3) lack of robustness in system diagnostics. The latter issue (3) is the main focus of this paper. This work presents an algorithm for the design of active fault detection and isolation (FDI) tests that provide rigorous guarantees of robustness in safety-critical systems. A semi-infinite program with implicit functions embedded is formulated with the objective of maximizing FDI effectiveness at the worst-case realization of uncertainty by manipulating admissible system inputs, while taking into account system safety constraints. This problem is solved locally and globally illustrating deficiencies in the performance of FDI tests designed for the mean values of anticipated uncertainty. The resulting solution is an optimally performing fault diagnostic test that guarantees system safety over the entire domain of uncertainty. This is illustrated using a benchmark three-tank system and further analyzed through Monte Carlo simulation and k-NN classification. (C) 2019 Elsevier Ltd. All rights reserved.